Reservation-based scheduling€¦ · Weakly-hard systems A task with 𝑚,𝑘weakly-hard timing...

1 | 57Embedded and Networked Systems

[email protected](appointment by email)

IN4343 Real-Time Systems, Lecture 11

Reservation-based scheduling

mailto:[email protected]


Sources

Some slides have been taken from Giorgio Buttazzo’s website:

http://retis.sssup.it/~giorgio/rts-MECS.html

Thank you Giorgio :)

Giorgio Buttazzo’s book, chapter 9

http://retis.sssup.it/~giorgio/

http://retis.sssup.it/~giorgio/rts-MECS.html


MPEG decoding

Frame execution

times distributionfor “Star Wars”

Note: it is a soft real-time system


Varying workload

Video playingMPEG standard encodes frames in "Group of Pictures" (GOP), consisting into 3 types of frames:• I frames (Inter-frames) include the entire content of a picture;• B frames, (Backwards predictive) look backwards at the I frames and P frames;• P frames (Predictive) looks forward at the frame, constantly comparing frame content.

PAL standard:

• frame rate = 25 fps

• decoding time: 2-20 ms

I-frames can take 10 timesmore than B-frames


What to do with varying workloads?

1. Calculate and use the worst-case execution time

Advantages• It is safe• Necessary for hard real-time systems

Disadvantages• It results in pessimistic analysis which is

far from reality• It leads to overprovisioning the system



2. Model it using more expressive task models

Advantages• It is safe but not pessimistic: you can use it

to obtain the WCRT of the task• Necessary for hard real-time systems

Disadvantages • It is too complex to derive such a model from a

general application• Some systems do not have such a regular pattern• It is hard to analyze such a complex workload

20 2 2 8

I frame B frame B frame P frame

𝑎𝑖,𝑗 𝑎𝑖,𝑗 + 𝛿𝑖,1 𝑎𝑖,𝑗 + 𝛿𝑖,2 𝑎𝑖,𝑗 + 𝛿𝑖,3 𝑎𝑖,𝑗 + 𝑇𝑖

𝑐𝑖,1 𝑐𝑖,2 𝑐𝑖,3 𝑐𝑖,4

𝜏𝑖 = 𝑐𝑖,1, 𝛿𝑖,1 , 𝑐𝑖,2, 𝛿𝑖,2 , 𝑐𝑖,𝑘𝑖 , 𝛿𝑖,𝑘𝑖 , 𝑇𝑖 , 𝐷𝑖

• Each pair 𝑐𝑖,𝑗 , 𝛿𝑖,𝑗 represents the workload of a frame

• 𝛿 is the intra-arrival-time of the frames

Multi-frame task model



3. Just use a smaller value than the WCET, but then handle task overruns!

Advantages• It is efficient since it allows having an analysis that is

closer to the average case performance of the system

• Allows using the existing analyses techniques

Disadvantages• It is unsafe: we may have deadline misses• If the value we assign is too small, many

“overruns” may happen. • Handling overruns increases the overheads

overruns

Overrun: happens when a task exceeds its expected utilization.


Load and design assumptions

System designed under worst-case assumptions

System designed under average-case assumptions


Consequences of overruns

A task overrun may not cause a deadline miss:

But in general, it may delay the execution of other tasks, causing a deadline miss:


What can go wrong if overruns are not controlled?

EDF may have domino effect:

one (or more) overrun(s) may result in a series of deadline misses

(exam example): Build an example of an EDF schedule with three jobs such that two jobs miss their deadline because of an overrun in the first job

(exam example): Consider the following task set scheduled by EDF. 1. How much overrun in 𝝉𝟏 will cause one deadline miss?2. How much overrun in 𝝉𝟏 will cause two deadline misses?

1 unit

0 5

15 17

25

10 0

16 17

25

6 10 0

17

25

8 10

3 units


What can go wrong if overruns are not controlled?

In FP, low-priority tasks may starve due to an overrun in high-priority tasks


Handling overruns: not-so-good solutions

• Terminate the execution of the task that overruns• It may cause data inconsistency

• Use fixed-priority scheduling and “pray”! • If a high-priority task overruns, lower-priority tasks may starve

• Exception handling mechanisms• These mechanisms have runtime overhead. Hence, they reduce

timing predictability


Handling overruns: better solutions

It is a mechanism to bound the resource consumption of a task

(and limit the interference to other tasks).

1. Performance degradation (also known as graceful degradation)• Execute a shorter version of the program

2. Resource reservation• Allows analyzing the WCRT despite possible

transient overruns• Isolates task’s overrun from each other

Fast and low qualityExample: a PID controller

Example: implement multiple versions:

Slow but high qualityExample: a model predictive controller is slow but can optimize control decisions

Middle ground Example: an LQG controller


Performance degradation

• Degrading functionality (reducing task execution time)

• Skipping specific jobs

• Increasing periods

The load can be decreased not only by rejecting tasks, but also by reducing their performance requirements.


Functional degradation

• In some applications, computation can be performed at different level of accuracy or quality of service (QoS):

“the higher the QoS, the longer the computation”

Examples:• Binary search algorithms• Image processing and computer graphics• Neural learning• Anytime control

Imprecise computation Multiple version


Imprecise computation

• In this model, each task 𝜏𝑖 = 𝐶𝑖 , 𝑇𝑖 , 𝐷𝑖 , 𝑀𝑖 , 𝑂𝑖 , 𝑤𝑖 is divided in two parts:

• a mandatory part with the worst-case execution time 𝑀𝑖

• an optional part: with the worst-case execution time 𝑂𝑖• 𝐶𝑖 = 𝑀𝑖 + 𝑂𝑖• 𝑤𝑖 is the importance weight of the optional part


Imprecise computation

• In this model, a schedule is said to be:• feasible, if all mandatory parts complete within 𝐷𝑖• precise, if also the optional parts are completed.

GOAL: minimize the average error


Multiple versions

• If a task does not comply with the imprecise computational model, another option is to implement a function in multiple versions (operational modes):

Decreasing quality of

service


Example: engine control task (in cars)

• In engine control, some tasks are activated at specific angles of the crankshaft.

• The activation rate of these tasks is proportional to the angular velocity 𝜔 of the engine:


Example: engine control task (in cars)

break


A solution for engine control tasks

rpm = rotation per minute.

Small period: 10mslarge period ~ 100ms

Reducing the number of functions


Job skipping

Periodic load can also be reduced by skipping some jobs, once in a while.

Many systems tolerate skips, if they do not occur too often:• multimedia systems (video reproduction)• inertial systems (robots)• Control systems • monitoring systems (sporadic data loss)


Example

• The system is overloaded, but tasks can be EDF-schedulable if 𝜏1 skips one instance every 3:


Weakly-hard systems

A task with 𝑚, 𝑘 weakly-hard timing constraint is feasible if and only if in every

window of k consecutive jobs of that task, at least m jobs meet their deadlines.

What is an (m, k) for 𝝉𝟏? (assume that the following pattern repeats forever)

𝜏20 100

Miss Miss Miss

0 10 20 30 40 50 60 70 80 90 100𝜏1

Miss

110 120

Miss

How about (3, 4)? No, because of 𝑱𝟏,𝟗 and 𝑱𝟏,𝟏𝟎

Can (6, 10) be an answer? Yes.

What is the smallest k if m = 2? 5

How about (2, 4)? No, because of 𝑱𝟏,𝟗 and 𝑱𝟏,𝟏𝟎 and 𝑱𝟏,𝟏𝟏


Weakly-hard systems




𝜏20 100

Miss Miss Miss

0 10 20 30 40 50 60 70 80 90 100𝜏1

Miss

110 120

Miss

What is the largest m if k = 6? 3


Weakly-hard systems




𝜏20 100

Miss Miss Miss

0 10 20 30 40 50 60 70 80 90 100𝜏1

Miss

What is the largest m if k = 8? 4

110 120

Miss


Weakly-hard systems




𝜏20 100

Miss Miss Miss

0 10 20 30 40 50 60 70 80 90 100𝜏1

Miss

What is the smallest non-zero m for any k > 1? 1 as in (1, 5)

What is the smallest k (with a non-zero m)? 4 as in (1, 4). Note that any k smaller than 3 will have m = 0

110 120

Miss


Weakly-hard systems



In general, can we say if a task set is (m, k) feasible, it will be (m-1, k) feasible too?

Yes. Just by definition: there must be “at least” m successful jobs in every window of k jobs.

In general, can we say if a task set is (m, k) feasible, it will be (m, k-1) feasible too?

No. The following task set is (1, 4) feasible but not (1, 3) feasible.

𝜏20 100

Miss Miss Miss

0 10 20 30 40 50 60 70 80 90 100𝜏1

Miss

110 120

Miss


Weakly-hard systems



In general, if a task set is (m, k) feasible, as long as we increase k or decrease m, it stays feasible

What (m, k) constraint represents a hard real-time system?

m must be equal with k, for example (1, 1) or (2, 2) or (100, 100)

New research directions: combining multiple (m, k) constraints:Example: At least 80% of the jobs must meet their deadlines in the long run, while the system cannot tolerate more than 3 misses in every 5 jobs:

(800, 1000) ∧ (2, 5)


Reservation-based scheduling

Resource reservation is a mechanism to bound the resource consumption of a task or a group of tasks

(and limit their interference on the other tasks).


Example: reservation-based scheduling

Reservation server 𝑺

𝜏1𝐶1 = 6𝑇1 = 30

Assume this is the pattern of available budget from a reservation server:

How is task 𝝉𝟏 scheduled within server 𝑺?

0 22 28 45 48 57 60

8 6 2 3 3

8 36 38

2 3 16

6 45 48 57 5836 380 30 60

More reservation is available than needed

The task is released but there is no budget to start its execution

What is the response time of 𝑱𝟏,𝟏? What is the WCRT of 𝝉𝟏?

6

28 A reservation shows when the processor can be assigned to a task


𝜏2: 𝐶1 = 16𝑇1 = 30

Assume this is the pattern of available budget from a reservation server:

How are tasks 𝝉𝟏 and 𝝉𝟐 scheduled in server 𝑺 when Rate Monotonic is used to schedule them inside the server?


0 24 28 45 48 50 60

22 4 8 3 10

22 30 38

What is the WCRT of 𝝉𝟏? What is the WCRT of 𝝉𝟐?

12

30

𝜏1: 𝐶1 = 5𝑇1 = 20

3 25

5 45 48 50 52

2

22 24 27

3

0 20 6040

0 30 6038

815

20 5228

81

Example: reservation-based scheduling

A reservation shows when the processor can be assigned to a task


Hierarchical scheduling

Resource reservation can be used to develop hierarchical systems, where each component is implemented within a reservation


Xen Project https://xenproject.org/

Hierarchical scheduling: hypervisor implementations

This is the most practical aspect of real-time systems course in your engineering life!

Familiarize with hypervisors

https://xenproject.org/


Hierarchical scheduling: hypervisor implementations

XtratuM hypervisorhttps://fentiss.com/products/hypervisor/

PikeOShttps://www.sysgo.com/products/pikeos-hypervisor/Uses offline scheduling for reservation servers.

Linux: Preempt-RThttps://www.linux.org/(implements constant-bandwidth server)

https://fentiss.com/products/hypervisor/

https://www.sysgo.com/products/pikeos-hypervisor/

https://www.linux.org/


Analyzing reservation-based scheduling

• To describe the time available in a reservation, we need to identify, for any interval [0, t], the minimum time allocated in the worst-case situation.

Supply bound function sbf(t):

minimum amount of time available in the reservation 𝑺 in every time interval of length t.


Example: static time partition

• Example of reservation providing 4 units every 10 (bandwidth = 0.4).

• Assume that the server is scheduled as the highest-priority entity in the system.

sbf(t)

4

8

6 10 16 20

sbf(t) shows the minimum amount of time available in the reservation 𝑺 in every time interval of length t.

Periodic reservation server 𝑆:

budget 𝑄𝑠 = 4Period 𝑃𝑠 = 10






sbf(t)

4

8

6 10 16 20


The minimum amount of time available every time interval of length 10 is 4.




sbf(t)

4

8

6 10 16 20



18

6






sbf(t)

4

8

6 10 16 20






Analysis under resource reservation + EDF

• Assume that tasks inside the server are scheduled by EDF.

We can use the Processor Demand Criterion as follows:

For each point in time where either the value of sbf(t) or dbf (t) changes, check if dbf(t) is smaller than sbf(t).


Faster test

• Assume that tasks inside the server are scheduled by EDF.

Design a faster sufficient schedulability test!

Replace sbf(t) with a lower bound, called

supply lower-bound function slbf(t):


Faster test: approximating supply lower-bound function with a line

• A simple supply bound function can have the form of a linear function (of time).

In other words, we want to approximate the sbf(t) with a linear equation:

Slope of this line is 𝛼

It cuts the horizontal axis at time Δ


Given a generic supply function sbf(t), the bandwidth 𝛼 is the equivalent to the slope computed for long intervals:

Faster test: approximating supply lower-bound function with a line


• For a periodic server with budget 𝑄𝑠 and period 𝑃𝑠 running at the highest priority (among other servers), we have:

Example: Periodic Server

Why did we need this assumption?

𝑄𝑠

𝑃𝑠is the utilization

of the server


Example: Periodic Server

• For a periodic server with budget 𝑄𝑠 and period 𝑃𝑠 running at an unknown priority, we have:


Observations about periodic servers

In a periodic server with bandwidth 𝛼, we have that:


Observations about periodic servers

A reservation can be wasted because of

• occasional load reduction due to early terminations

• wrong bandwidth allocation at design time

• application changes due to environmental changes


Next lecture introduces other type of servers


Step 1: open www.kahoot.it in your browser (phone or laptop)Step 2: enter the pin code and then a nickname

http://www.kahoot.it/


Which partitioning solution results in a feasible RM-schedulable?

𝝉𝒊 𝑻𝒊 𝑼𝒊

1 5 0.2

2 10 0.1

3 20 0.69

4 25 0.3

A: Core 1: {𝜏1, 𝜏2} , Core 2: {𝜏3, 𝜏4}

B: Core 1: {𝜏1, 𝜏2, 𝜏3} , Core 2: {𝜏4}

C: Core 1: {𝜏1, 𝜏3} , Core 2: {𝜏2, 𝜏4}

D: Core 1: {𝜏1, 𝜏2, 𝜏4} , Core 2: {𝜏3}

Answer: D


What is the smallest k for Task 1 when m = 3?

𝜏20 100

Miss

0 10 20 30 40 50 60 70 80 90 100𝜏1

Miss

Weakly hard system (m = 3, k = ?)

Miss Miss

Answer: k = 7

𝜏20 100

Miss

0 10 20 30 40 50 60 70 80 90 100𝜏1

Miss Miss Miss


If this was a repeatable pattern of a periodic server, what could be its possible period and budget?


0 22 28 45 48 55 60

8 6 2 3 5

8 36 38

Period is 20Budget is 8

Reservation server 𝑺𝑷𝒔 = 𝟐𝟎𝑸𝒔 = 𝟖

0 22 28 45 48

8 6 2 3

8 36 38

20 40 600

55 60

5

What are the parameters of this periodic server?


5

5 20 40 600 55

Which sbf(t) represents this server?

35

sbf(t)

5

10

30 35 55 7050

sbf(t)

10

20

25 40 604520

Reservation server 𝑺Period 𝑷𝒔 = 𝟐𝟎Budget 𝑸𝒔 = 𝟓The server has an unknown priority

A: B:


1 2

3

4

1

5

2

5

2

Label shows WCET

Reservation-based scheduling€¦ · Weakly-hard systems A task with 𝑚,𝑘weakly-hard timing...

Documents

Transcript of Reservation-based scheduling€¦ · Weakly-hard systems A task with 𝑚,𝑘weakly-hard timing...